Abstract: An iterative method based on orthogonal arrays is presented in this paper. And this method is used as the primary means to construct Cartesian authentication codes with k sources and n authentication symbols, where k and n are two arbitrary positive integers. When each source occurs equally often and encoding rule distribution is uniform, the probabilities of successful impersonation and substitution attack are 1/n. Compared with the Cartesian authentication codes constructed by Descartes product, the authentication codes produced with iterative means have much less encoding rules, when they contain the same parameters k and n.